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They are not all build from axioms but from definition (apart from some models of natural numbers, or you go back to ZFC). Like C is build from R^2, R from the
by andi999 5y ago
They are not all build from axioms but from definition (apart from some models of natural numbers, or you go back to ZFC). Like C is build from R^2, R from the powerset of Q, Q from integer^2, integer from natural numbers.
Otherwise you do not easily know if your axioms are actually consistent.
- mkl 5y agoYes, but what I meant is that there are axioms at the base of this structure, so everything is ultimately built on them. Some people put axiom foundations higher up too, like axiomatic real numbers.
- andi999 5y agoYes, there are of course axioms, but if you have a rich enough set of axioms like zfc, then one should stop piling more axioms (if not absolutely necessary). So of course the question is existence in zfc